The number 34680

Q: Is 34680 a prime number?

No. 34680 = 2^3 × 3 × 5 × 17^2, so it is divisible by 2.

34680 is a composite number with 48 divisors. Its prime factorisation is $2^{3}$ × 3 × 5 × $17^{2}$ . Divisors (48): 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40 … 34680.

Number

Pick any whole number from 1 to 100,000.

34680 = 2^{3} \times 3 \times 5 \times 17^{2}

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How to work it out

1
34680 has no famous special property in the usual lists (prime, square, cube, triangular, Fibonacci, palindrome, perfect), but it is still a composite number.
2
34680 is composite. Its prime factorisation is
$34680 = 2^{3} \times 3 \times 5 \times 17^{2}$
3
The divisors add up to 110520; without 34680 itself that is 75840, so 34680 is abundant (75840 is more than 34680). Euler's totient φ(34680) = 8704 numbers up to 34680 share no factor with it.
4
The digits of 34680 add up to 21, and repeating that until one digit is left gives the digital root 3. The Collatz sequence (halve if even, else 3n+1) takes 67 steps to reach 1.

LaTeX source of the formulas on this page

\[ 34680 = 2^{3} \times 3 \times 5 \times 17^{2} \]

34680 at a glance

Property	Value
Type	composite
Number of divisors	48
Sum of divisors	110520
Euler totient φ(n)	8704
Square	1202702400
Cube	41709719232000
Square root	186.225670 (= 34√30)
Digit sum / digital root	21 / 3
Collatz steps to 1	67
Scientific notation	3.468 × $10^{4}$

34680 in other forms

Form	Value
In words	thirty-four thousand six hundred and eighty
Binary (base 2)	1000011101111000
Octal (base 8)	103570
Hexadecimal (base 16)	8778
Base 3	1202120110
As time	34680 seconds = 9 h 38 min 0 s

Is 34680 divisible by 2 to 12?

Divisor	Answer	Rule
2	Yes (34680 ÷ 2 = 17340)	A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8).
3	Yes (34680 ÷ 3 = 11560)	A number is divisible by 3 if the digits add up to a multiple of 3.
4	Yes (34680 ÷ 4 = 8670)	A number is divisible by 4 if the last two digits make a multiple of 4.
5	Yes (34680 ÷ 5 = 6936)	A number is divisible by 5 if the last digit is 0 or 5.
6	Yes (34680 ÷ 6 = 5780)	A number is divisible by 6 if it is divisible by both 2 and 3.
7	No (remainder 2)	A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7.
8	Yes (34680 ÷ 8 = 4335)	A number is divisible by 8 if the last three digits make a multiple of 8.
9	No (remainder 3)	A number is divisible by 9 if the digits add up to a multiple of 9.
10	Yes (34680 ÷ 10 = 3468)	A number is divisible by 10 if the last digit is 0.
11	No (remainder 8)	A number is divisible by 11 if the alternating sum of the digits is a multiple of 11.
12	Yes (34680 ÷ 12 = 2890)	A number is divisible by 12 if it is divisible by both 3 and 4.

Questions

Is 34680 a prime number?

No. 34680 = $2^{3}$ × 3 × 5 × $17^{2}$ , so it is divisible by 2.

What are the factors of 34680?

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 20, 24, 30, 34, 40, 51, 60, 68, 85, 102, 120, 136, 170, 204, 255, 289, 340, 408, 510, 578, 680, 867, 1020, 1156, 1445, 1734, 2040, 2312, 2890, 3468, 4335, 5780, 6936, 8670, 11560, 17340, 34680.

What is 34680 in binary?

1000011101111000 (hexadecimal 8778, octal 103570).

What is the square root of 34680?

About 186.2257, exactly 34√30.

Is 34680 divisible by 3?

Yes. Its digits add up to 21, a multiple of 3.

What is special about the number 34680?

It is a composite number with 48 divisors.